Sure, there are problems with all systems.
Fundamentally, if people can't agree, it's hard to make a system where things get done.
But in Europe, most of which has a multiparty indirect system (UK/Germany/Scandi/Spain), you have a government formed from a coalition of parties that doesn't have a majority against it. And you still have a semblance of voting for a particular leader, even though you're not actually. You know pretty well who will be your country's head if you vote for a particular party, at least until they resign.
The problem of small parties is normally dealt with by having a lower limit. For instance in Denmark and Sweden there's a 2/4% minimum proportion. That way you need some support to be represented, though of course a 10% voting bloc can still swing itself around like it's 20%. That's hard to quantify anyway, because it's a matter of how much they value various policies.
If you look at the US at the moment, you have a President that people voted for, who basically can't pass the laws that he promised everyone. You have ridiculous things like filibusters, where you can abuse the rules if you can't get what you want. You have seats that are safe in the election, but contested in the primaries. You have all sorts of issues about who is funding the parties. Children in school can see it's ridiculous.
Time to try a few new things. Proportional representation is just one thing, obviously nothing is guaranteed. Will be hard though, with the current system.